ISD techniques have evolved [1]}, [2]}, [3]}, [4]}, [5]} by first introducing [1]} collision/subset-sum techniques
whose purpose is to produce for codes of rate close to 1, all codewords of some small weight, and later on by substantially improving them by using on top of that for instance representation techniques [4]}. These algorithms come very handy in our case for devising the function Create\(N,w,{{P}}\)  that we need. In the previous section, we have explored what could be achieved by the very first techniques of this type taken from [8]}, [2]}. We are
going to explain now what can be gained by using [4]}, [5]}.
It is convenient here to formalize the basic step used in the previous section which can be explained by the following function

 Input: \({{L}}_1 \subseteq \mathbb {F}_2^n\) , \({{L}}_2\subseteq \mathbb {F}_2^n\) , \(w \in \llbracket 1, n \rrbracket \) , \({\mathbf {H}}\in \mathbb {F}_2^{\ell \times n}\)
